Scandinavia is out of my scope, but I can comment on Ireland and England.

There are very few medical sources for 10th century England and Ireland. This is partially because medical schools are not around quite yet. In both places, though, your best bet for medical care would most likely be a convent or monastery, especially if the battle is taking place in the country where doctors are scarce. I think that the chance of survival would be the same in each country, especially because of the lack of medical education. Monks and nuns had medical knowledge, but it was usually very basic. The essentials were needed to treat each other when they became sick or injured, and so there was usually at least one cleric that had some medical knowledge (see Hildegard von Bingen). That being said, treatment would have been very basic. Cleaning the wound, adding a salve or ointment, and bandaging smaller wounds, and setting or amputating larger wounds. However, clerics were forbidden from spilling blood, so amputation might not be as common. Infection rates, as you can imagine, would be incredibly high, but the use of honey in Ireland and England would have helped. Honey acts as a barrier (at least when applied and bandaged) and it has antibacterial properties to combat infection. There is also a chance that the injured might have access to local empirics that would have utilized similar techniques.